I just discovered another way that also seems to update your wall automatically when you post new photos. On your Facebook wall there is a button "Options" below the status update box. Clicking on this will reveal another button "Setting". There you can add your Picasa site.

Uploading a picture to my Picasa account automatically triggered an update on my wall. However, unlike the built in Facebook photos, no album is created to view previous pictures although friends can still comment on your wall post.

Edit Well isn't Facebook annoying. Literally the day after I post this, the feature has been removed with the following notice:

The Imported Stories feature is no
longer available. Most of the sites
supported by this feature now allow
you to publish stories to Facebook
directly from the site.

I've just discovered Showzey, which claims to let you manage all your online photos (certainly those stored within Picasa web albums, Facebook and Flickr) in one place. It doesn't seem to automatically sync (so doesn't quite meet the requirements in the question) and seems a tad slow to me, but may well be worth a look as a central point for managing what gets shared with whom, across several platforms.

There is a Windows app called "Social Folders" that is very close to doing it. The only problem is that it has separate folders for each service (ie one for Picasa, one for Facebook) so you would have a bunch duplicates on your PC.